Problem: Little Pig got 24 bricks and built a wall at the end his garden. The wall was 4 bricks high and 6 bricks across. Little Pig painted the wall. He painted the sides of the bricks that were not touching the ground and not touching other bricks. How many sides of bricks did Little Pig have to paint?
Math Topic/Concept: Geometry, find a pattern, logic, spatial visualization.
Materials: rectangle blocks, work sheet
Classroom Use: (Introductory/Developmental/Evaluation)
Grade: 3
Grade Cluster: (EarlyElem/LateElem/MS-Jr.High/EarlyHS/LateHS)
Illinois Goal: 9
Standard: 9.C.2
Applied? (1-4): 2
Source: The Problem Solver 3, Creative Publications
Answer: 62
Strategies Listed: Draw a picture, make a table, look at a simpler problem.
Solution: Draw a picture of a brick wall four bricks high
and six bricks across. Count the number of bricks on the front (24)
back (24) left side (4), right side (4), and top (6).
The total is 62 bricks.
Other solution methods (if any)*: Make a table starting
with a simpler problem. Start with four bricks in the wall.
Count the exposed sides and find 17 sides. Add four bricks and count
the sides and find 26 sides. Continue adding four bricks. Find
the pattern of increasing the sides by nine each time.
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Extensions or related problems*: Change the wall to two high and 12 across, or change the number of bricks.
Intended rubric or assessment method: State (ISAT) rubric
Write-up submitted by: Diana Kent
Problem: Propose this task: “Each of you will construct geometric figures (polygons) based on specific descriptions and within the stated restrictions on the data card you receive.” (On the data cards, provide “restrictions” for the characteristics of the polygon; for example, “I have 2 sets of parallel sides, all of my corners form right angles, and I might have two lines of symmetry but not 3 or 4.”)
1. Consider what polygon you might have, then write down your guess
and explain what information on the card helped you make that guess.
2. Using the appropriate tools, construct the figure precisely and
neatly. Label your dimensions (in. or cm.), and name each of the
sides (A, B, C, etc.)
Math Topic/Concept: identifying and constructing polygons
Materials: paper & pencil, rules, protractors (optional: grid paper)
Classroom Use: (Evaluation)
Classroom use comments*: Prior to this activity, review the basic shapes of polygons and discuss their characteristics. Provide data cards (a different one for each student).
Grade: 4
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9.B.2 and 9.C.2
Applied? (1-4): 2 (possibly 3 if extension problem is used)
Source: various worksheets, ideas, and suggestions from textbooks and conferences
Answer: various, according to data cards created by teacher and according to dimensions selected by students. Check student products for accuracy.
Strategies Listed: prediction, logical thinking, measurement, application of information
Solution: Students will analyze the information on the data cards and consider the basic characteristics of specific geometric figures. They will record their guesses and then use appropriate tools to draw accurate figures on paper. During and after the construction, students will check the data card to match their figures to all descriptions and restrictions listed on the card.
Other solution methods (if any)*: computer-generated drawings
Extensions or related problems*: Use flip, slide, and turn with favorite polygon to create a pattern. Explain (in writing) how the characteristics of the chosen polygon affect the outcome of the pattern (e.g. circular, linear, overlapping, lines of symmetry, extended, etc.)
Intended rubric or assessment method: Analytical Scoring Scale (Jim Olsen, WIU)
Write-up submitted by: Rebecca Cummins (Westmer CUSD 203)
Problem: If you are given five different colors of LinkerCubes, how many different pentominos can you make?
Math Topic/Concept: Geometry
Materials: 60 LinkerCubes , 2 centimeter grid paper, paper, pencils, crayons
Classroom Use: (Introductory)
Classroom use comments*: Were the students able to find
all 12 Pentominos?
Were they able to record each Pentomino?
Grade: Third
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9.A.2, 9.C.2
Applied? (1-4): 1
Source: 20 Thinking Questions for LinkerCubes, Creative Publications
Answer: 12
Strategies Listed: Make the shapes and record shapes on the Grid Paper. Then check for duplicates because of flipping or turning.
Solution:
Intended rubric or assessment method: informal assessment
Write-up submitted by: Beth Reedy, Third Grade, Harding Elementary, Monmouth, Illinois
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001